旋转平移协变卷积网络在医学图像分析中的应用
Roto-Translation Covariant Convolutional Networks for Medical Image Analysis
摘要：
我们提出了一个使用$SE(2)$群卷积进行旋转和平移协变深度学习的框架。特殊欧几里得运动群$SE(2)$的群积描述了两个旋转平移的级联如何导致净旋转平移。我们通过$SE(2)$组卷积层将这种几何结构编码到卷积神经网络（CNN）中，这些卷积层适合标准的2D CNN框架，并且允许在不需要数据增强的情况下一般处理旋转的输入样本。我们引入三层：提升层，其将2D（向量值）图像提升为$SE(2)$图像，即，域为$SE(2)$的3D（向量值）数据;来自和去往$SE(2)$图像的组卷积层;以及从$SE(2)$图像到2D图像的投影层。提升和组卷积层是$SE(2)$协变的（输出与输入旋转平移）。最后的投影层是旋转上的最大强度投影，使完整的CNN旋转不变。我们用组织病理学、视网膜成像和电子显微镜中的三个不同问题表明，使用所提出的组CNN，可以实现最先进的性能，而不需要通过旋转进行数据增强，并且与依赖增强的标准CNN相比，性能有所提高。
英文摘要：
We propose a framework for rotation and translation covariant deep learning using $SE(2)$ group convolutions. The group product of the special Euclidean motion group $SE(2)$ describes how a concatenation of two roto-translations results in a net roto-translation. We encode this geometric structure into convolutional neural networks (CNNs) via $SE(2)$ group convolutional layers, which fit into the standard 2D CNN framework, and which allow to generically deal with rotated input samples without the need for data augmentation. We introduce three layers: a lifting layer which lifts a 2D (vector valued) image to an $SE(2)$-image, i.e., 3D (vector valued) data whose domain is $SE(2)$; a group convolution layer from and to an $SE(2)$-image; and a projection layer from an $SE(2)$-image to a 2D image. The lifting and group convolution layers are $SE(2)$ covariant (the output roto-translates with the input). The final projection layer, a maximum intensity projection over rotations, makes the full CNN rotation invariant. We show with three different problems in histopathology, retinal imaging, and electron microscopy that with the proposed group CNNs, state-of-the-art performance can be achieved, without the need for data augmentation by rotation and with increased performance compared to standard CNNs that do rely on augmentation.
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